Abstract.
In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in an approximate transformation of the equation governing wave motion over an uneven bottom to an equation for a flat one for which the exact solution exists. The calculation is one space dimensional, and so corresponds to long trenches or banks under wide rivers or oceans.
Graphical abstract
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Karczewska, P. Rozmej, E. Infeld, Phys. Rev. E 90, 012907 (2014)
E. Infeld, A. Karczewska, G. Rowlands, P. Rozmej, Exact solitonic and periodic solutions of the extended KdV equation, arXiv:1612.03847
T.R. Marchant, N.F. Smyth, J. Fluid Mech. 221, 263 (1990)
G.I. Burde, A. Sergyeyev, J. Phys. A: Math. Theor. 46, 075501 (2013)
A. Karczewska, P. Rozmej, L. Rutkowski, Phys. Scr. 89, 054026 (2014)
T. Taniuti C.C. Wei, J. Phys. Soc. Jpn. 24, 941 (1968)
A. Karczewska, P. Rozmej, E. Infeld, Phys. Rev. E 92, 053202 (2015)
A. Karczewska, P. Rozmej, E. Infeld, G. Rowlands, Phys. Lett. A 381, 270 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Rowlands, G., Rozmej, P., Infeld, E. et al. Single soliton solution to the extended KdV equation over uneven depth. Eur. Phys. J. E 40, 100 (2017). https://doi.org/10.1140/epje/i2017-11591-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2017-11591-7